For finitary set functors preserving inverse images, recursive coalgebras of Paul Taylor are proved to be precisely those for which the system described by always halts in finitely many steps.
@article{ITA_2007__41_4_447_0, author = {Ad\'amek, Ji\v r\'\i\ and L\"ucke, Dominik and Milius, Stefan}, title = {Recursive coalgebras of finitary functors}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {41}, year = {2007}, pages = {447-462}, doi = {10.1051/ita:2007028}, mrnumber = {2377973}, zbl = {pre05301991}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2007__41_4_447_0} }
Adámek, Jiří; Lücke, Dominik; Milius, Stefan. Recursive coalgebras of finitary functors. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) pp. 447-462. doi : 10.1051/ita:2007028. http://gdmltest.u-ga.fr/item/ITA_2007__41_4_447_0/
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